We study Rabi oscillations (RO) in case of asymmetric monolayer graphene (asymmetry between sub-lattices makes it a gapped system) in two different cases – resonance (conventional RO) and off-resonance (anomalous RO). In an earlier work, we have shown that graphene exhibits anomalous RO far from resonance, attributable to the pseudo-spin degree of freedom of graphene. The anomalous Rabi frequency (ARF) is typically much smaller than the conventional one. In case of asymmetric graphene, the ARF differs from the symmetric value by an additive constant equal to twice the gap parameter. This shift is found to be numerically one to two orders of magnitude larger than the ARF for symmetric graphene. However, the conventional Rabi frequency (CRF) is not significantly modified as a result of asymmetry.